When an electric field is applied across a conductor the electrons move at essentially the same time - a kind of organized step sequence - by one electron moving (left for example) it provides a spot for the electron to the right to move in to.

So, what the link and you are saying is that the electrons are normally just in the electron cloud, but when Voltage is applied the electrons are bouncing from one atom to the next atom in the conductor. I had a hard time understanding the math, but i think that it is saying.

I have one more question, is current or amperage the speed at witch the electrons flow.

Current is defined by movement of charge. One ampere of current is defined as the movement of one coulomb of charge ( about 6.23 X 10^18 electrons) past a fixed point in one second.

The speed at which individual electrons travel in the conductor isn't really defined by the current. But, looking at the conductor, it is easy to say that electrons have to move faster in a small conductor than in a large one, just to move the same amount of charge in a given unit of time.